In some types of reactors a profile thermocouple rod is place between the two quartz tubes. Set points for the profile thermocouples are used to control the reactor heaters in an attempt to maintain a pre-specified wafer temperature. The profile thermocouples measure a temperature that is different than the wafer temperature. Therefore, it is important to know the relationship between the thermocouple and wafer temperatures in order to properly control the heaters. The LPCVD Thermal Analyzer provides information regarding this relationship by incorporating a simple model that determines the profile thermocouple temperatures as part of the reactor thermal simulation.

In the LPCVD Thermal Analyzer, the thermocouples are considered to be small enough that they have negligible effect on the temperature of the surrounding reactor elements. In addition, the transient thermal response of the thermocouples is considered to be much faster than any of the other elements in the reactor. If heat conduction and convection from the thermocouple are neglected then the absorbed and emitted radiation from the surface of the thermocouple must balance according to the relationship

(7–15)

where is the irradiation on the thermocouple and is the temperature of the thermocouple. In the LPCVD Thermal Analyzer, the thermocouple temperatures are computed after the temperature distribution in the reactor has been found. Because the solution for the reactor temperatures is known, the radiosities leaving the surfaces of the two quartz tubes are known and can be used to compute the irradiation on the thermocouple. The expression for the thermocouple irradiation is of the form

(7–16)

where is the radiosity leaving a surface element on the quartz tube and represents the shapefactor from the thermocouple to the surface element on the quartz tube. Shape factors between the thermocouples and quartz tube elements are computed by treating each profile thermocouple as a small segment of the cylindrical ring located between the two quartz (inner and outer) tubes at the axial grid point closest to the user-specified position of the thermocouple.